title: Application of the random ball test for calibrating slope-dependent errors in profilometry measurements.
abstract: Optical profilometers such as scanning white light interferometers and confocal microscopes provide high-resolution measurements and are widely utilized in many fields for measuring surface topography. Slope-dependent systematic errors can be present in the measurement and can be the same order of magnitude as features on the surface to be measured. We propose a self-calibration technique, the random ball test (RBT), for calibrating slope-dependent errors of such instruments. The calibration result can be used to compensate future measurements of similar spherical geometries such as profiles of refractive microlenses. A simulation study validates the approach and shows that the RBT is effective in practical limits. We demonstrate the calibration on a 50× confocal microscope and find a surface slope-dependent bias that increases monotonically with the magnitude of the surface slope and is as large as ∼800  nm at a surface slope of 12°. The uncertainty of the calibration is smaller than the observed measurement bias and is dominated by residual random noise. Effects such as drift and ball radius uncertainty were investigated to understand their contribution to the calibration uncertainty.
authors.forename: Yue
authors.initials: Y
authors.lastname: Zhou
authors.forename: Young-Sik
authors.initials: YS
authors.lastname: Ghim
authors.forename: Ali
authors.initials: A
authors.lastname: Fard
authors.forename: Angela
authors.initials: A
authors.lastname: Davies